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Sam · 2022年10月27日

如何判断BPV不相等

  1. CFA III
  2. Fixed Income

NO.PZ2018120301000015

问题如下：

The second project for Serena is to help Trey immunize a $20 million portfolio of liabilities. The liabilities range from 3.00 years to 8.50 years with a Macaulay duration of 5.34 years, cash flow yield of 3.25%, portfolio convexity of 33.05, and basis point value (BPV) of $10,505. Serena suggested employing a duration-matching strategy using one of the three AAA rated bond portfolios presented in Exhibit 2.


Which portfolio in Exhibit 2 fails to meet the requirements to achieve immunization for multiple liabilities?

选项：

A.

Portfolio A

B.

Portfolio B

C.

Portfolio C

解释：

Correct Answer: A

A is correct. The two requirements to achieve immunization for multiple liabilities are for the money duration (or BPV) of the asset and liability to match and for the asset convexity to exceed the convexity of the liability. Although all three portfolios have similar BPVs, Portfolio A is the only portfolio to have a lower convexity than that of the liability portfolio (31.98, versus 33.05 for the $20 million liability portfolio), and thus, it fails to meet one of the two requirements needed for immunization.

老师您好，到目前为止，我看到的题里面,BPV 相近的，按照出题者思路，都是算作相等。依照何老师在讲述duration matching的例题中，判断portfolio是否合适，固然使用了三个条件来判断，但听得出是有已重要程度来判断：BPV最重要，convexity大小次之，因为先通过BPV排除了一个portfolio，然后再根据convexity来筛出合适的portfolio。那在这题中，根据BPV判断，portfolio A 的BPV差距最大，明显可以初步判断A不行。但是答案居然给出的方向是convexity的原因（虽然的确是不符合条件3）。

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1 个答案

pzqa015 · 2022年10月28日

嗨，从没放弃的小努力你好：


是这样的同学，何老师讲的条件是BPV完全相等，这样是最好的，但是实践过程中，很难做到BPV完全相等，一般我们认为二者近似相等即可（客观题，这样来判断）。这道题说负债的BPV是10505，三个portfolio的BPV分别是10524、10506、10516，它们与负债BPV的差异，在个位数到十位数不等。对于一个以万为单位计量的数字，相差千分之甚至万分之几，是可以认为近似相等的，所以，其实这三个portfolio的BPV都满足条件，要用convexity来选出最佳选项。

如果主观题让写免疫的条件，对于BPV这个条件，我们还是要写相等，而不能是近似相等的。

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